Convergence of Regular Spiking and Intrinsically Bursting Izhikevich Neuron Models as a Function of Discretization Time with Euler Method Harish Gunasekaran a,1 , Giacomo Spigler b,1 , Alberto Mazzoni b , Enrico Cataldo c , Calogero Maria Oddo b,* a University of Pisa, Pisa, Italy b The Biorobotics Institute, Scuola Superiore Sant’Anna, Pisa, Italy c Physics Department, University of Pisa, Pisa, Italy Abstract This study investigates the trade-off between computational efficiency and accuracy of Izhikevich neuron models by numerically quantifying their conver- gence to provide design guidelines in choosing the limit time steps during a discretization procedure. This is important for bionic engineering and neuro- robotic applications where the use of embedded computational resources requires the introduction of optimality criteria. Specifically, the regular spiking (RS) and intrinsically bursting (IB) Izhikevich neuron models are evaluated with step inputs of various amplitudes. We analyze the convergence of spike sequences generated under different discretization time steps (10μs to 10ms), with respect to an ideal reference spike sequence approximated with a discretization time step of 1μs. The differences between the ideal reference and the computed spike sequences were quantified by Victor-Purpura (VPd) and van Rossum (VRd) distances. For each distance, we found two limit discretization times (dt 1 and dt 2 ), as a function of the applied input and thus firing rate, beyond which the convergence is lost for each neuron model. Keywords: Convergence, Izhikevich Neuron Model, Discretization, Euler method, Victor-Purpura Distance, van Rossum Distance, CUSUM * Corresponding author Email address: calogero.oddo@santannapisa.it (Calogero Maria Oddo) 1 These authors contributed equally to this work Preprint submitted to Neurocomputing June 20, 2018